Precision measurement of the
e
þ
e
!
K
þ
K
ð
Þ
cross section
with the initial-state radiation method at
B
A
B
AR
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
M. J. Lee,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
A. Khan,
8
V. E. Blinov,
9a,9c
A. R. Buzykaev,
9a
V. P. Druzhinin,
9a,9b
V. B. Golubev,
9a,9b
E. A. Kravchenko,
9a,9b
A. P. Onuchin,
9a,9c
S. I. Serednyakov,
9a,9b
Yu. I. Skovpen,
9a,9b
E. P. Solodov,
9a,9b
K. Yu. Todyshev,
9a,9b
A. N. Yushkov,
9a
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
G. M. Vitug,
11
C. Campagnari,
12
M. Franco Sevilla,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
W. S. Lockman,
13
A. J. Martinez,
13
B. A. Schumm,
13
A. Seiden,
13
D. S. Chao,
14
C. H. Cheng,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
B. G. Pushpawela,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
†
W. H. Toki,
17
B. Spaan,
18
R. Schwierz,
19
D. Bernard,
20
M. Verderi,
20
S. Playfer,
21
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
I. Garzia,
22a,22b
E. Luppi,
22a,22b
L. Piemontese,
22a
V. Santoro,
22a
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
S. Martellotti,
23
P. Patteri,
23
I. M. Peruzzi,
23,
‡
M. Piccolo,
23
M. Rama,
23
A. Zallo,
23
R. Contri,
24a,24b
E. Guido,
24a,24b
M. Lo Vetere,
24a,24b
M. R. Monge,
24a,24b
S. Passaggio,
24a
C. Patrignani,
24a,24b
E. Robutti,
24a
B. Bhuyan,
25
V. Prasad,
25
M. Morii,
26
A. Adametz,
27
U. Uwer,
27
H. M. Lacker,
28
P. D. Dauncey,
29
U. Mallik,
30
C. Chen,
31
J. Cochran,
31
W. T. Meyer,
31
S. Prell,
31
A. E. Rubin,
31
A. V. Gritsan,
32
N. Arnaud,
33
M. Davier,
33
D. Derkach,
33
G. Grosdidier,
33
F. Le Diberder,
33
A. M. Lutz,
33
B. Malaescu,
33,
§
P. Roudeau,
33
A. Stocchi,
33
L. L. Wang,
33,
∥
G. Wormser,
33
D. J. Lange,
34
D. M. Wright,
34
J. P. Coleman,
35
J. R. Fry,
35
E. Gabathuler,
35
D. E. Hutchcroft,
35
D. J. Payne,
35
C. Touramanis,
35
A. J. Bevan,
36
F. Di Lodovico,
36
R. Sacco,
36
G. Cowan,
37
J. Bougher,
38
D. N. Brown,
38
C. L. Davis,
38
A. G. Denig,
39
M. Fritsch,
39
W. Gradl,
39
K. Griessinger,
39
A. Hafner,
39
E. Prencipe,
39
K. Schubert,
39
R. J. Barlow,
40,
¶
G. D. Lafferty,
40
E. Behn,
41
R. Cenci,
41
B. Hamilton,
41
A. Jawahery,
41
D. A. Roberts,
41
R. Cowan,
42
D. Dujmic,
42
G. Sciolla,
42
R. Cheaib,
43
P. M. Patel,
43,
*
S. H. Robertson,
43
P. Biassoni,
44a,44b
N. Neri,
44a
F. Palombo,
44a,44b
L. Cremaldi,
45
R. Godang,
45,
**
P. Sonnek,
45
D. J. Summers,
45
X. Nguyen,
46
M. Simard,
46
P. Taras,
46
G. De Nardo,
47a,47b
D. Monorchio,
47a,47b
G. Onorato,
47a,47b
C. Sciacca,
47a,47b
M. Martinelli,
48
G. Raven,
48
C. P. Jessop,
49
J. M. LoSecco,
49
K. Honscheid,
50
R. Kass,
50
J. Brau,
51
R. Frey,
51
N. B. Sinev,
51
D. Strom,
51
E. Torrence,
51
E. Feltresi,
52a,52b
M. Margoni,
52a,52b
M. Morandin,
52a
M. Posocco,
52a
M. Rotondo,
52a
G. Simi,
52a
F. Simonetto,
52a,52b
R. Stroili,
52a,52b
S. Akar,
53
E. Ben-Haim,
53
M. Bomben,
53
G. R. Bonneaud,
53
H. Briand,
53
G. Calderini,
53
J. Chauveau,
53
Ph. Leruste,
53
G. Marchiori,
53
J. Ocariz,
53
S. Sitt,
53
M. Biasini,
54a,54b
E. Manoni,
54a
S. Pacetti,
54a,54b
A. Rossi,
54a
C. Angelini,
55a,55b
G. Batignani,
55a,55b
S. Bettarini,
55a,55b
M. Carpinelli,
55a,55b,
††
G. Casarosa,
55a,55b
A. Cervelli,
55a,55b
F. Forti,
55a,55b
M. A. Giorgi,
55a,55b
A. Lusiani,
55a,55c
B. Oberhof,
55a,55b
E. Paoloni,
55a,55b
A. Perez,
55a
G. Rizzo,
55a,55b
J. J. Walsh,
55a
D. Lopes egna,
56
J. Olsen,
56
A. J. S. Smith,
56
R. Faccini,
57a,57b
F. Ferrarotto,
57a
F. Ferroni,
57a,57b
M. Gaspero,
57a,57b
L. Li Gioi,
57a
G. Piredda,
57a
C. Bu
̈
nger,
58
O. Gru
̈
nberg,
58
T. Hartmann,
58
T. Leddig,
58
C. Voß,
58
R. Waldi,
58
T. Adye,
59
E. O. Olaiya,
59
F. F. Wilson,
59
S. Emery,
60
G. Hamel de Monchenault,
60
G. Vasseur,
60
Ch. Ye
`
che,
60
F. Anulli,
61
D. Aston,
61
D. J. Bard,
61
J. F. Benitez,
61
C. Cartaro,
61
M. R. Convery,
61
J. Dorfan,
61
G. P. Dubois-Felsmann,
61
W. Dunwoodie,
61
M. Ebert,
61
R. C. Field,
61
B. G. Fulsom,
61
A. M. Gabareen,
61
M. T. Graham,
61
C. Hast,
61
W. R. Innes,
61
P. Kim,
61
M. L. Kocian,
61
D. W. G. S. Leith,
61
P. Lewis,
61
D. Lindemann,
61
B. Lindquist,
61
S. Luitz,
61
V. Luth,
61
H. L. Lynch,
61
D. B. MacFarlane,
61
D. R. Muller,
61
H. Neal,
61
S. Nelson,
61
M. Perl,
61
T. Pulliam,
61
B. N. Ratcliff,
61
A. Roodman,
61
A. A. Salnikov,
61
R. H. Schindler,
61
A. Snyder,
61
D. Su,
61
M. K. Sullivan,
61
J. Va’vra,
61
A. P. Wagner,
61
W. F. Wang,
61
W. J. Wisniewski,
61
M. Wittgen,
61
D. H. Wright,
61
H. W. Wulsin,
61
V. Ziegler,
61
W. Park,
62
M. V. Purohit,
62
R. M. White,
62,
‡‡
J. R. Wilson,
62
A. Randle-Conde,
63
S. J. Sekula,
63
M. Bellis,
64
P. R. Burchat,
64
T. S. Miyashita,
64
E. M. T. Puccio,
64
M. S. Alam,
65
J. A. Ernst,
65
R. Gorodeisky,
66
N. Guttman,
66
D. R. Peimer,
66
A. Soffer,
66
S. M. Spanier,
67
J. L. Ritchie,
68
A. M. Ruland,
68
R. F. Schwitters,
68
B. C. Wray,
68
J. M. Izen,
69
X. C. Lou,
69
F. Bianchi,
70a,70b
F. De Mori,
70a,70b
A. Filippi,
70a
D. Gamba,
70a,70b
S. Zambito,
70a,70b
L. Lanceri,
71a,71b
L. Vitale,
71a,71b
F. Martinez-Vidal,
72
A. Oyanguren,
72
P. Villanueva-Perez,
72
H. Ahmed,
73
J. Albert,
73
Sw. Banerjee,
73
F. U. Bernlochner,
73
H. H. F. Choi,
73
G. J. King,
73
R. Kowalewski,
73
M. J. Lewczuk,
73
T. Lueck,
73
I. M. Nugent,
73
J. M. Roney,
73
R. J. Sobie,
73
N. Tasneem,
73
T. J. Gershon,
74
P. F. Harrison,
74
T. E. Latham,
74
H. R. Band,
75
S. Dasu,
75
Y. Pan,
75
R. Prepost,
75
and S. L. Wu
75
(
B
A
B
AR
Collaboration)
PHYSICAL REVIEW D
88,
032013 (2013)
1550-7998
=
2013
=
88(3)
=
032013(28)
032013-1
Ó
2013 American Physical Society
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie, CNRS/IN2P3,
F-74941 Annecy-Le-Vieux, France
2
Departament ECM, Facultat de Fisica, Universitat de Barcelona, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
9b
Novosibirsk State University, Novosibirsk 630090, Russia
9c
Novosibirsk State Technical University, Novosibirsk 630092, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California 91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, USA
18
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
19
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern-und Teilchenphysik, D-01062 Dresden, Germany
20
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
21
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
22a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
22b
Dipartimento di Fisica e Scienze della Terra, Universita
`
di Ferrara, I-44122 Ferrara, Italy
23
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24a
INFN Sezione di Genova, I-16146 Genova, Italy
24b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
25
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Universita
̈
t Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
28
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, D-12489 Berlin, Germany
29
Imperial College London, London SW7 2AZ, United Kingdom
30
University of Iowa, Iowa City, Iowa 52242, USA
31
Iowa State University, Ames, Iowa 50011-3160, USA
32
Johns Hopkins University, Baltimore, Maryland 21218, USA
33
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN2P3/CNRS et Universite
́
Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
34
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
35
University of Liverpool, Liverpool L69 7ZE, United Kingdom
36
Queen Mary, University of London, London E1 4NS, United Kingdom
37
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
38
University of Louisville, Louisville, Kentucky 40292, USA
39
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
40
University of Manchester, Manchester M13 9PL, United Kingdom
41
University of Maryland, College Park, Maryland 20742, USA
42
Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
43
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
44a
INFN Sezione di Milano, I-20133 Milano, Italy
44b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
45
University of Mississippi, University, Mississippi 38677, USA
46
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
47a
INFN Sezione di Napoli, I-80126 Napoli, Italy
47b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
48
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
49
University of Notre Dame, Notre Dame, Indiana 46556, USA
50
Ohio State University, Columbus, Ohio 43210, USA
51
University of Oregon, Eugene, Oregon 97403, USA
52a
INFN Sezione di Padova, I-35131 Padova, Italy
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032013 (2013)
032013-2
52b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
53
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
54a
INFN Sezione di Perugia, I-06123 Perugia, Italy
54b
Dipartimento di Fisica, Universita
`
di Perugia, I-06123 Perugia, Italy
55a
INFN Sezione di Pisa, I-56127 Pisa, Italy
55b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
55c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
56
Princeton University, Princeton, New Jersey 08544, USA
57a
INFN Sezione di Roma, I-00185 Roma, Italy
57b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
58
Universita
̈
t Rostock, D-18051 Rostock, Germany
59
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
60
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
61
SLAC National Accelerator Laboratory, Stanford, California 94309, USA
62
University of South Carolina, Columbia, South Carolina 29208, USA
63
Southern Methodist University, Dallas, Texas 75275, USA
64
Stanford University, Stanford, California 94305-4060, USA
65
State University of New York, Albany, New York 12222, USA
66
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
67
University of Tennessee, Knoxville, Tennessee 37996, USA
68
University of Texas at Austin, Austin, Texas 78712, USA
69
University of Texas at Dallas, Richardson, Texas 75083, USA
70a
INFN Sezione di Torino, I-10125 Torino, Italy
70b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
71a
INFN Sezione di Trieste, I-34127 Trieste, Italy
71b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
72
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
73
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
74
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
75
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 21 June 2013; published 27 August 2013)
A precise measurement of the cross section for the process
e
þ
e
!
K
þ
K
ð
Þ
from threshold to an
energy of 5 GeV is obtained with the initial-state radiation (ISR) method using
232 fb
1
of data collected
with the
BABAR
detector at
e
þ
e
center-of-mass energies near 10.6 GeV. The measurement uses the
effective ISR luminosity determined from the
e
þ
e
!
þ
ð
Þ
ISR
process with the same data set.
The corresponding lowest-order contribution to the hadronic vacuum polarization term in the muon
magnetic anomaly is found to be
a
KK;
LO
¼ð
22
:
93
0
:
18
stat
0
:
22
syst
Þ
10
10
. The charged kaon form
factor is extracted and compared to previous results. Its magnitude at large energy significantly exceeds
the asymptotic QCD prediction, while the measured slope is consistent with the prediction.
DOI:
10.1103/PhysRevD.88.032013
PACS numbers: 13.40.Em, 13.60.Hb, 13.66.Bc, 13.66.Jn
I. INTRODUCTION
The measurement of the
e
þ
e
!
K
þ
K
ð
Þ
cross sec-
tion presented in this paper takes place in the context of a
precision measurement of
R
¼
ð
e
þ
e
!
hadrons
Þ
=
ð
e
þ
e
!
þ
Þ
at low energy. Integrals involving
R
enter the calculations of the hadronic contribution to vac-
uum polarization (VP). Uncertainties on VP are a limiting
factor in precise comparisons of data with the Standard
Model expectations, such as the value of the muon mag-
netic moment anomaly
a
. The analysis makes use of
several data-driven techniques to measure efficiencies
and constrain systematic uncertainties below the 1% level.
Accurate parameters for the
resonance are determined
and the charged kaon form factor is extracted for the first
*
Deceased.
†
Present address: University of Tabuk, Tabuk 71491, Saudi
Arabia.
‡
Also at Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
§
Present address: Laboratoire de Physique Nucle
́
aire et de
Hautes Energies, IN2P3/CNRS, Paris, France.
∥
Also at Institute of High Energy Physics, Beijing, China.
¶
Present address: University of Huddersfield, Huddersfield
HD1 3DH, United Kingdom.
**
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
††
Also at Universita
`
di Sassari, Sassari, Italy.
‡‡
Present address: Universidad Te
́
cnica Federico Santa Maria,
Valparaiso, Chile 2390123.
PRECISION MEASUREMENT OF THE
...
PHYSICAL REVIEW D
88,
032013 (2013)
032013-3
time in a large energy range, from the
K
þ
K
production
threshold to 5 GeV.
Unlike previous measurements, which were performed
through energy scans, the present analysis uses the initial-
state radiation (ISR) method [
1
–
4
]. The
e
þ
e
!
K
þ
K
ð
Þ
cross section at the reduced energy
ffiffiffiffi
s
0
p
is
deduced from the measured spectrum of
e
þ
e
!
K
þ
K
ð
Þ
ISR
events produced at the center-of-mass
(c.m.) energy
ffiffiffi
s
p
. The reduced energy is related to the
energy
E
of the ISR photon in the
e
þ
e
c.m. frame by
s
0
¼
s
ð
1
2
E
=
ffiffiffi
s
p
Þ
, and it is equal to the mass
m
KK
of the
hadronic final state, or
m
KK
if an additional photon
from final-state radiation (FSR) has been emitted.
The cross section for the process
e
þ
e
!
K
þ
K
ð
Þ
is
related to the
ffiffiffiffi
s
0
p
spectrum of
e
þ
e
!
K
þ
K
ð
Þ
ISR
events through
dN
K
þ
K
ð
Þ
ISR
d
ffiffiffiffi
s
0
p
¼
dL
eff
ISR
d
ffiffiffiffi
s
0
p
"
KK
ð
ffiffiffiffi
s
0
p
Þ
0
KK
ð
Þ
ð
ffiffiffiffi
s
0
p
Þ
;
(1)
where
dL
eff
ISR
=d
ffiffiffiffi
s
0
p
is the effective ISR luminosity,
"
KK
is
the full acceptance for the event sample, and
0
KK
ð
Þ
is the
‘‘bare’’ cross section for the process
e
þ
e
!
K
þ
K
ð
Þ
(including final-state radiative effects), from which the
leptonic and hadronic vacuum-polarization contributions
are excluded. In contrast to most measurements based on
the ISR method, the effective ISR luminosity does not rely
on the theoretical radiator function [
1
–
4
], which describes
the probability to emit an ISR photon of energy
E
in a
given angular acceptance, or on the external measurement
of the data luminosity. Instead, the effective ISR luminos-
ity is determined from the measurement of the
e
þ
e
!
þ
ð
Þ
ISR
spectrum with the same data sample,
through a relation similar to Eq. (
1
) where the
e
þ
e
!
þ
cross section is given by QED. In this manner
several systematic uncertainties cancel. In particular, the
cross section measurement is mostly insensitive to higher-
order ISR corrections and other theoretical uncertainties
that affect the kaon and muon channels equally. The
method used in this analysis has been developed for the
precision measurement of the
e
þ
e
!
þ
ð
Þ
cross
section and is expounded in Ref. [
5
].
This paper is organized as follows. In Sec.
II
,we
describe the data samples used in the analysis and the event
selection. In Sec.
III
, selection efficiencies and the corre-
sponding corrections based on differences between data
and Monte Carlo (MC) simulation are presented.
Section
IV
describes backgrounds. Section
V
is dedicated
to the unfolding of the mass spectrum, while Sec.
VI
describes the acceptance corrections applied to the cross
section. Finally, Sec.
VII
reports the results for the cross
section and kaon form factor from threshold to 5 GeV,
and includes the
K
þ
K
contribution to the anomalous
magnetic moment of the muon.
II. SAMPLES AND EVENT SELECTION
Signal events are characterized by two charged-particle
tracks and a high-energy photon, all required to lie within
the detector acceptance. In addition, in order to control
the overall efficiency to high precision, it is found neces-
sary to include higher-order radiation. The next-to-
leading order (NLO) is sufficient to reach accuracies of
10
3
, so the analysis considers
KK
as well as
KK
final states, where the additional photon can be either ISR
or FSR.
The data were produced at the SLAC National
Accelerator Laboratory at the PEP-II
e
þ
e
collider, oper-
ated at and 40 MeV below the peak of the
ð
4
S
Þ
resonance,
ffiffiffi
s
p
¼
10
:
58 GeV
. The analysis is based on
232 fb
1
of
data collected with the
BABAR
detector, described in detail
in Ref. [
6
]. Charged-particle tracks are measured with a
five-layer double-sided silicon vertex tracker (SVT)
together with a 40-layer drift chamber (DCH), both inside
a 1.5 T superconducting solenoid magnet. Photons are
assumed to originate from the primary vertex defined by
the charged tracks of the event, and their energy and
position are measured in a CsI(Tl) electromagnetic calo-
rimeter (EMC). Charged-particle identification (PID) uses
the ionization energy loss (
d
E=
d
x
) in the SVT and DCH,
the Cherenkov radiation detected in a ring-imaging device
(DIRC), the shower energy deposit in the EMC (
E
cal
), and
the shower shape in the instrumented flux return (IFR) of
the magnet. The IFR system is composed of modules of
resistive-plate chambers interspaced with iron slabs,
arranged in a layout with a barrel and two endcaps.
Signal and background ISR processes are simulated with
the
AFKQED
event generator based on Ref. [
7
]. The signal
KK
ð
Þ
ISR
sample corresponds to about 30 times the
integrated luminosity of the data. The main ISR photon,
ISR
, is generated within the angular range [
min
¼
20
,
max
¼
160
] in the c.m. system,
1
wider than the geomet-
rical acceptance of the detector. Additional radiation from
the initial state is generated with the structure function
method [
8
] in the collinear approximation, while additional
final-state photons are generated with the
PHOTOS
[
9
]
program. A minimum-mass requirement
m
K
þ
K
ISR
>
8 GeV
=c
2
, applied at generation, limits the emission of a
second hard photon in simulation. Background processes
e
þ
e
!
q
q
(
q
¼
u
,
d
,
s
,
c
) are generated with the
JETSET
[
10
] generator, and
e
þ
e
!
þ
with the
KORALB
[
11
]
program. The response of the
BABAR
detector is simulated
using the
GEANT4
[
12
] package. In addition, since the
additional ISR generated by
AFKQED
is inadequate,
large samples of MC events at the four-momentum level,
dedicated to specific ISR studies, are produced with the
nearly-exact NLO
PHOKHARA
[
13
] generator.
1
Unless otherwise stated, starred quantities are measured in
the
e
þ
e
c.m. and un-starred quantities in the laboratory.
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032013 (2013)
032013-4
A. Topological selection
Two-charged-particle ISR events are selected by requir-
ing a photon with an energy
E
>
3 GeV
in the
e
þ
e
c.m.
and laboratory polar angle with respect to the
e
beam in
the range [0.35–2.4] rad, and exactly two tracks of opposite
charge, each with momentum
p>
1 GeV
=c
and within the
angular range [0.40–2.45] rad. If more than one photon is
detected, the ISR photon is assumed to be the candidate
with the highest
E
. The charged-particle tracks are
required to have at least 15 hits in the DCH, to originate
within 5 mm of the collision axis (distance of closest
approach
doca
xy
<
5mm
) and within 6 cm from the
beam spot along the beam direction (
j
z
j
<
6cm
), and
to extrapolate to the DIRC and IFR active areas, in order
to exclude low-efficiency regions. Events can be accom-
panied by any number of reconstructed tracks not satisfy-
ing the above criteria, and any number of additional
photons. To ensure a rough momentum balance at the
preselection level (hereafter called ‘‘preselection cut’’),
the ISR photon is required to lie within 0.3 rad of the
missing momentum of all the tracks (or of the tracks plus
the other photons).
B. Kaon identification
To select
KK
candidates, the two tracks are required to
be identified as kaons. Kaon identification (
K
-ID) proceeds
from an optimization between efficiency and misidentifi-
cation of particles of other types
ð
e; ; ; p
Þ
as kaons.
Electron contamination is strongly reduced by a criterion
based on a combination of
E
cal
and
d
E=
d
x
. In addition,
kaons are positively selected through a likelihood estima-
tor
L
based on the
d
E=
d
x
in the DCH and SVT and on the
Cherenkov angle in the DIRC. Tracks whose number of
associated photons in the DIRC is not sufficient to define a
Cherenkov ring (
N
DIRC
<
3
) are rejected. Pions and pro-
tons are rejected through selection criteria on likelihood
ratios:
L
K
=
ð
L
K
þ
L
Þ
>
0
:
9
and
L
K
=
ð
L
K
þ
L
p
Þ
>
0
:
2
,
respectively. Kaons are further required to fail muon iden-
tification. To maximize the
K
-ID efficiency, the veto
against the muon background relies on a tight muon selec-
tor, where muons are identified by an energy deposit in the
EMC consistent with a minimum ionizing particle (MIP),
and topological requirements in the IFR (penetration, num-
ber of hits, and shower width). A
K
-ID efficiency of 80% is
achieved. The probabilities to misidentify a muon or pion
as a kaon are below 10% and are measured in the data, as
described in Sec.
III C 2
. The proton misidentification
probability is 5% or less and is taken from simulation.
C. ISR kinematic fit with an additional photon
Following the method described in Ref. [
5
] for the
analysis of the
and
processes, the event defini-
tion is enlarged to include the radiation of one photon
in addition to the already required ISR photon. Two
kinematic fits to the
e
þ
e
!
KK
ð
Þ
ISR
hypothesis are
performed:
(i) If an additional photon is detected in the EMC with
energy
E
>
20 MeV
, its energy and angles are used
in a three-constraint fit. We call this an ‘‘FSR’’ fit,
although the extra photon can be either from FSR or
from ISR at large angle. In case multiple extra
photons are detected, the FSR fit is performed using
each photon in turn and the fit with the smallest
2
FSR
is retained.
(ii) For every event, an additional photon from ISR at
small angle is assumed to be emitted along either
the
e
þ
or the
e
beam direction. The corresponding
so-called two-constraint ISR fit ignores additional
photons measured in the EMC and returns the
energy
E
add ISR
of the fitted collinear ISR photon.
In both cases, the constrained fit uses the measured
ISR
direction, and momenta and angles of the two tracks, along
with their covariance matrix, to solve the four-momentum
conservation equations. The kaon mass is assumed for the
two charged particles. The energy of the primary ISR
photon is not used in either fit. Each event is characterized
by the
2
values of the two kinematic fits, except for the
12.5% of the candidates with no extra measured photons,
for which only the
2
from the ISR fit (
2
ISR
) is available.
The
K
þ
K
invariant mass
m
KK
is obtained using the
fitted parameters of the two kaons from the ISR fit if
2
ISR
<
2
FSR
, and from the FSR fit in the reverse case.
Most events appear at small values of both
2
ISR
and
2
FSR
, as shown on the two-dimensional
2
distribution
(Fig.
1
), but the tails along the axes clearly indicate events
with additional radiation: small-angle ISR along the
2
FSR
axis (with large fitted photon energies at large values of
2
FSR
), and FSR or large-angle ISR along the
2
ISR
axis
(with large measured photon energies at large values of
0
2
4
6
8
10
12
024681012
1
10
10
2
10
3
ln(
χ
2
ISR
+1)
ln(
χ
2
FSR
+1)
no add. photon
add.‘FSR’
add.ISR
no add.Rad.
BG region
trk rec + interactions + more add. rad.
FIG. 1 (color online). The two-dimensional
2
distribution for
the
KK
ð
Þ
ISR
data sample in the
½
0
:
98
–
5
GeV
=c
2
range of the
fitted
KK
mass, where different interesting regions are defined.
The line labeled ‘‘no add. photon’’ corresponds to events with no
detected additional photon, which are characterized by the
2
ISR
value only.
PRECISION MEASUREMENT OF THE
...
PHYSICAL REVIEW D
88,
032013 (2013)
032013-5
2
ISR
). Events along the diagonal do not satisfy either
hypothesis and result from either the finite resolution
of the kaon-track measurement or the direction of the
primary ISR photon, or possibly from additional radiation
of more than one photon. Events affected by secondary
interactions also lie along the diagonal. Multibody back-
ground is expected to populate the region where both
2
are large, and, consequently, a background (‘‘BG’’) region
is defined in the two-dimensional
2
plane, as indicated
in Fig.
1
.
For the cross section measurement, the
KK
ð
Þ
ISR
candidates are required to satisfy a ‘‘tight’’ selection
ln
ð
2
ISR
þ
1
Þ
<
3
. In order to study efficiencies, back-
grounds and mass resolution, we define a ‘‘loose’’ selec-
tion, given by the full two-dimensional
2
plane except for
the BG-labeled region. We refer to the region within the
loose selection but excluded by the tight selection as the
‘‘intermediate’’ region.
D. Raw mass spectrum and angular distribution
in the
K
þ
K
frame
Figure
2
shows the
K
þ
K
mass spectrum measured in
the data with the tight
2
selection, without background
subtraction or correction for acceptance. The spectrum
exhibits distinct features. Besides the prominent
reso-
nance at
1
:
02 GeV
=c
2
, other structures are visible in the
½
1
:
6
–
2
:
5
GeV
=c
2
mass region, as well as signals at the
J=
c
and
c
ð
2
S
Þ
resonances. These features are examined
in Sec.
VII
.
Since the background is small in the
region, as dis-
cussed in Sec.
IV
, one can readily verify that the angular
distribution in the
KK
center-of-mass frame behaves as
expected for a decaying vector-particle with helicity one.
Figure
3
shows the distributions of the cosine of the angle
trk
between the ISR photon and the charged tracks in the
KK
center-of-mass frame, for data and MC. The two
distributions are consistent with each other and follow
the expected
sin
2
trk
shape.
III. EFFICIENCY AND DATA-MC CORRECTIONS
FOR DETECTOR SIMULATION
The mass-dependent overall acceptance
"
KK
is deter-
mined with the full
AFKQED
plus
GEANT4
simulation, with
corrections applied to account for observed differences
between data and MC. Through specific studies, we deter-
mine the ratios of the efficiencies
"
i
obtained with the same
methods in data and simulation for the trigger, tracking,
PID, and
2
selection, and we apply them as mass-
dependent corrections to the measured
m
KK
spectrum.
Corrections to the geometrical acceptance are treated sepa-
rately in Sec.
VI
, as most corrections cancel in the
KK
ð
Þ
cross section measurement using the effective luminosity
from
ð
Þ
ISR
data.
The event efficiency corrected for detector effects is thus
"
¼
"
MC
"
data
trig
"
MC
trig
!
"
data
track
"
MC
track
!
"
data
PID
"
MC
PID
!
"
data
2
"
MC
2
!
:
(2)
1
10
10
2
10
3
0.98
1
1.02
1.04
1.06
1.08
1.1
m
KK
(GeV/c
2
)
Events / (0.5 MeV/c
2
)
1
10
10
2
10
3
1.5
2
2.5
3
3.5
4
4.5
5
m
KK
(GeV/c
2
)
Events / (20 MeV/c
2
)
FIG. 2 (color online). The
K
þ
K
invariant mass spectrum for the data sample, after the tight
2
selection:
mass region (left),
masses above
m
(right).
0
200
400
600
800
1000
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
|cos
θ
γ
trk
|
Events / 0.01
FIG. 3 (color online). Distributions of the absolute value of the
cosine of the angle between the ISR photon and the charged
tracks in the
KK
center-of-mass, for data (black points) and MC
(blue histogram). The
KK
mass range is from 1.01 to
1
:
03 GeV
=c
2
. The MC is normalized to the number of events
in the data.
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032013 (2013)
032013-6
The mass-dependent corrections
C
i
¼ð
"
data
i
="
MC
i
Þ
are dis-
cussed below. Most trigger, tracking, and PID inefficien-
cies arise from a geometrical effect, namely the overlap of
the two tracks in the DCH, EMC, or IFR. To avoid
correlations between the
C
i
terms, the efficiencies are
determined sequentially, with minimal requirements on
the subsequent step. Trigger efficiency is measured on
enlarged signal samples selected without a requirement
on the actual number of reconstructed tracks. Tracking
efficiency is measured with events that have passed the
triggers. PID efficiencies and misidentification probabil-
ities are measured with two-track events. Biases associated
with the efficiency determination, which result from the
measurement method, are studied with MC and are nor-
malized to data through data-to-MC comparison of char-
acteristic distributions once the physics origin of the bias is
identified. Since the data sample in the
peak region is so
pure, efficiencies are measured in the restricted mass range
1
:
0
<m
KK
<
1
:
05 GeV
=c
2
and extrapolated to higher
mass regions, where large backgrounds preclude direct
measurements. Extrapolation is performed using the
KK
ð
Þ
ISR
MC to sample the corrections
C
i
determined
in the restricted phase space as functions of the relevant
variables. Details of the procedure applied to determine
each
C
i
correction term are given below.
A. Trigger and filter efficiency corrections
Trigger and filter efficiencies are determined in data and
MC using complementary triggers. Several sets of criteria
(triggers) are applied to each of three levels—hardware
(L1), software (L3) and event filter (EF)—and the response
of each is recorded with the event. In addition, a prescaled
sample is retained regardless of whether any trigger is
satisfied. The efficiencies of all triggers can therefore be
cross calibrated with the others. These are all multipurpose
triggers common to
BABAR
, with none specifically
designed to retain two-track ISR events.
Events for the trigger studies are selected through the
one-constraint (1C) fit designed for tracking studies (see
below) applied to the one- or two-prong sample. The
‘‘primary’’ track is required to be identified as a kaon
with momentum
p>
1 GeV
=c
, but otherwise minimal
requirements are imposed on track quality to avoid corre-
lations with the tracking efficiency measurement.
Inefficiencies of the hardware (L1) and software (L3)
triggers are found to be below
10
4
and
ð
3
:
5
0
:
2
Þ
%
,
respectively, for data in the vicinity of the
peak. They
are well reproduced by simulation, and the deviation from
unity of the data/MC ratio for the L3 trigger efficiency is
found to be
ð
0
:
3
1
:
6
Þ
10
3
, with no significant
variation with
m
KK
. The online event filter introduces an
inefficiency of
ð
1
:
2
0
:
1
Þ
10
3
in data, slightly under-
estimated by MC; a correction of
ð
0
:
6
0
:
2
Þ
10
3
is
applied. Biases on L3 and filter efficiency measurements
are observed in MC at a few per mil level. They are due to
pairs of noninteracting, minimum ionizing kaons, whose
tracks overlap both in the DCH and EMC. For such events,
the tracking-based triggers are degraded while, simulta-
neously, the triggers based on EMC deposits are enhanced.
The biases are calibrated with data using the fractions of
double-MIP deposits in the EMC. They are maximal at the
mass due to the kinematics of the
resonance. The
related uncertainties on
C
trig
are
0
:
7
10
3
under the
peak and are extrapolated to about
0
:
5
10
3
at larger
masses. At threshold, the uncertainties related to the muon
background subtraction in the data sample dominate, and
the systematic error on
C
trig
reaches
1
:
0
10
3
.
B. Tracking efficiency correction
A 1C kinematic fit is used to select
K
þ
K
ISR
events for
tracking efficiency studies. The fit is performed on an
enlarged tracking sample that includes events with one or
two tracks. The fit uses as input only one kaon-identified
good track (called ‘‘primary’’) and the ISR photon, and the
momentum vector of the second kaon is predicted from
four-momentum conservation. The predicted kaon is
required to lie within the tracking acceptance. Only kine-
matically reconstructed
K
þ
K
masses in the
resonance
region (
1
:
00
<m
KK
<
1
:
05 GeV
=c
2
) are selected in order
to reduce the non-kaon background in the tracking sample
to the 1% level.
The rate of in-acceptance predicted tracks that are
actually reconstructed in the tracking system, with a charge
opposite to that of the primary kaon, determines the kaon
tracking efficiency. The method yields the intrinsic track-
ing inefficiency, which is mostly due to interactions in the
detector material or kaon decays in flight. In addition to the
uncorrelated track loss, a local reduction of the individual
track efficiency is induced by the overlap of the tracks in
the DCH. The tracking efficiency as a function of the
signed angular difference between the positive and nega-
tive tracks in the transverse plane
¼
þ
exhib-
its a dip at small positive values of
both in data and
MC, which is characteristic of track overlap. This effect
has been studied in detail in data and simulation for the
þ
and
þ
final states [
5
]. The same features are
observed for
K
þ
K
, although the
mass selection applied
to the kaon tracking sample precludes
from reaching
values larger than 0.15 rad.
Some difference between data and MC is observed in the
magnitude of the effect, as seen in Fig.
4
. The
depen-
dence of the data/MC correction is fitted with the func-
tional form observed over the full
range for muons and
pions: besides a flat component due to the intrinsic ineffi-
ciency, a double Gaussian is used to describe the sharp
asymmetric structure related to the track overlap, located at
0
:
1 rad
. As the magnitude of the overlap effect
varies with mass, studies of the peak inefficiency are
performed with MC on the kaon sample, and, in parallel,
on the muon (pion) samples of
(
) data and MC
PRECISION MEASUREMENT OF THE
...
PHYSICAL REVIEW D
88,
032013 (2013)
032013-7
events. The general mass dependence of the peak ineffi-
ciency is similar for all two-track ISR channels: a maxi-
mum of about 1%–2% around the region of maximum
overlap, and a slow decrease to a plateau at higher masses.
In the muon sample, where efficiencies can be measured
both in data and MC over the full mass range, the data/MC
ratio of peak inefficiencies is found to be independent of
mass. This validates the extrapolation of the track overlap
effect in
KK
, measured at the
mass, to higher masses
according to the mass dependence of the peak inefficiency
in MC. The latter is obtained in wide mass ranges, and the
resulting
C
track
correction is shown in Fig.
5
as a function
of mass, where discontinuities reflect the statistical
fluctuations of the peak inefficiency values, and errors
are fully correlated within the wide mass bins. The correc-
tion increases from 3.0% at threshold to about 4.5% in the
region, and it decreases to around 1.5% at high masses.
The probability of losing the two tracks in a correlated
way, also induced by the track overlap, and the probability
for having an extra reconstructed track, are found to be
well reproduced by MC in this analysis and small data/MC
differences of
0
:
8
10
3
and
1
:
2
10
3
, respectively, are
included in the systematic uncertainties. Uncertainties on
the bias from the primary-track tagging induce a system-
atic error of
1
:
1
10
3
. Together with the uncertainties on
the mass dependence of the overlap correction, the domi-
nant contribution to the systematic error is related to the
model used to describe the correction as a function of
.
The total systematic uncertainty for the
C
track
correction is
smaller than 0.3% below
1
:
05 GeV
=c
2
, increasing to about
1% at high mass.
C. Particle ID efficiency corrections
Separation of ISR two-body processes
e
þ
e
!
x
þ
x
ð
Þ
ISR
(
x
¼
e
,
,
,
K
,
p
) from each other relies
on PID. The specific studies conducted to determine the
kaon-ID efficiency for data and MC, as well as the
!
‘
K
’ and
!
‘
K
’ misidentification probabilities, are
described below. Electron misidentification as a kaon is
negligible, as well as data/MC corrections for proton
misidentification.
1.
K
-ID efficiency
The method to determine the kaon-ID efficiencies makes
use of the two-body ISR sample itself, where one of the
produced charged particles is tagged as a kaon and the
identification of the second track is probed (‘‘tag-and-
probe’’ method). The PID sample is selected through 1C
)
2
(GeV/c
KK
m
1
1.5
2
2.5
3
3.5
4
4.5
5
MC
track
ε
/
data
track
ε
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Stat. Error MC KK
Total Error
)
2
(GeV/c
KK
m
1
1.02
1.04
1.06
1.08
1.1
MC
track
ε
/
data
track
ε
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Stat. Error MC KK
Total Error
FIG. 5 (color online). The data/MC correction for the tracking efficiency as a function of
m
KK
. The red error bars show the (small)
statistical errors from the sampling, whereas the blue ones show the total errors (including the errors from the fit). The figure on the
right is a zoom of the figure on the left in the
resonance region.
(rad)
φ
δ
-0.1 5
-0.1
-0.0 5
0
0.0 5
0. 1
0.15
MC
track
ε
/
data
track
ε
0.7
0.75
0.8
0.85
0.9
0.95
1
FIG. 4 (color online). Fit of the data/MC correction for the
tracking efficiency (per event, i.e., for the two tracks) as a
function of
. The function for the fit is a constant plus two
Gaussians. The central values of the Gaussians are fixed at
0.1 rad. The red band indicates the errors computed from the
covariance matrix of the fit parameters.
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032013 (2013)
032013-8